Point-Set Topology
A 24-module path through point-set topology, in study order from foundations to the frontier.
Modules
- Metric Spaces
- Open and Closed Sets in Metric Spaces
- Topological Spaces and Open Sets
- Bases and Subbases for a Topology
- Closure, Interior, and Boundary
- Limit Points and Sequences
- Continuity of Maps
- Homeomorphisms
- The Subspace Topology
- The Product Topology
- The Quotient Topology
- Hausdorff and Separation Axioms
- Dense Sets and Separability
- Connected Spaces
- The Intermediate Value Theorem Topologically
- Path-Connectedness
- Compact Spaces and Open Covers
- The Heine-Borel Theorem
- Sequential Compactness
- The Tychonoff Theorem
- Completeness and Cauchy Sequences
- The Baire Category Theorem
- The Fundamental Group
- Covering Spaces